Regardless of the particular type, function and configuration of an aircraft, one must always design an aircraft with a certain and preferably optimum degree of static and dynamic stability and control in all degrees of freedom. The particular amount of pitch, roll and yaw stability will depend upon the particular use and application for which the aircraft is being designed. Ordinarily, optimum performance characteristics throughout the entire flight envelope and, more particularly, at the low speed and high speed extremes of such envelope, are extremely difficult to achieve since designs directed to the attainment of optimum performance at such extremes are somewhat incompatible. The traditional design approach normally involves selecting one particular flight condition or a portion of the flight envelope such as cruise flight, high speed flight, climb characteristics, or range, and then designing the aircraft to achieve the desired stability characteristics by establishing a particular size, shape and configuration which optimizes stability for this particular flight condition or region. Obviously, stability and control optimization in one region of the flight envelope will not necessarily produce optimization in other regions of the flight envelope and therefore the resulting design choice must necessarily represent a compromise selected on the basis of yielding the best overall performance characteristics throughout the entire flight envelope.
As with longitudinal and directional stability, an optimum degree of lateral stability throughout the entire flight envelope is advantageous. This may be accomplished by use of dihedral in the design of the wing geometry. Lateral stability involves maintaining control over the rolling moments about an aircraft's longitudinal axis. The major control over the rolling moments associated with a particular aircraft design is usually an aileron system which, when deflected assymmetrically, will alter the wings' spanwise lift distribution in such a way that a net rolling moment is created. However, and importantly, a secondary control over an aircraft's rolling moments can be obtained through control over the sideslip angle since, for certain wing geometries, sideslip will likewise alter the wings spanwise lift distribution to create a net rolling moment. The phenomenon of rolling moment due to sideslip is defined as dihedral effect. An aircraft is said to have stable dihedral effect if a negative rolling moment is created as the result of positive sideslip. This definition is somewhat arbitrary but springs from the fact that stable dihedral effect is required for complete dynamic lateral or roll stability. Incorporation of dihedral into wing surfaces therefore provides an additional means of obtaining control over the rolling moment due to sideslip.
The rolling moment due to sideslip is mainly created by the wing dihedral angle .GAMMA. which is positive when the wing tip chord lies above the root chord. The dihedral angle associated with an aircraft is illustrated in FIG. 1 and represents the angle between the horizontal and a line midway between the upper and lower surfaces of the wing as indicated. In a sideslip, the angle-of-attack of the forward wing will be higher than the angle-of-attack of the trailing wing thereby creating a lift on the leading wing that will be greater than the lift on the trailing wing. This creates a rolling moment about the longitudinal axis of the aircraft as illustrated in FIG. 1. The dihedral effect is measured by the change in rolling moment coefficient C.sub.l per degree change in sideslip angle .beta.. The criterion of dihedral effect is the slope of the curve of rolling moment coefficient plotted against yaw or sideslip and is given as the derivative dC.sub.l /d.beta.. The value of this derivative varies almost directly with wing dihedral angle at the approximate rate of DC.sub.l /d.beta.=0.0002 .DELTA..GAMMA.. In evaluating a wind or a whole aircraft to obtain the total value of dC.sub.l /d.beta., the term effective dihedral is used. One degree of effective dihedral corresponds to a value of dC.sub.l /d.beta.=-0.0002/deg.
It has been found that dihedral effect will be somewhat invarient with change in wing angle-of-attack for straight wings, but will change rapidly with angle-of-attack for swept wings. The effect of deflected flaps on dihedral effect can likewise be large if the flap hinge line has any sweep. The dihedral effect for aircraft having swept-wing planforms therefore becomes a function of lift coefficient. This means that aircraft with swept-back wings will have an increasing dihedral effect with corresponding increases in lift coefficient, while aircraft with swept-forward wings will have a decreasing dihedral effect. Typical variations in the rolling moment derivative or dihedral effect parameter dC.sub.l d.beta. with respect to lift coefficient are illustrated in FIG. 2 for the case of a swept-forward and swept-back wing. For example, if the geometric dihedral of the swept-back wing airplane is set to yield a desired dC.sub.l /d.beta. value at a low lift coefficient, that is, at high speed or negative pitch, then the aircraft with a swept-back wing will be in danger of having excessive effective dihedral when operating at high lift coefficients, that is, at low speeds or +G maneuvering, while the aircraft with a swept-forward wing will most probably encounter negative dihedral effect at high lift coefficients, that is, at low speeds. To estimate the overall effective dihedral for an aircraft, then, requires considerable experience in allowing for many complex variables.
Since the dihedral effect for swept-wing aircraft is tied to the lift coefficient of the wing, swept-wing aircraft encounter a different problem regarding roll-yaw stability as compared to a straight wing aircraft. This is because the aerodynamic coefficients of roll stability do vary from the on-design condition when the swept wings' lift coefficient varies from the on-design lift coefficient. The result is that the swept-back wing design has too much effective dihedral at higher-than-design lift coefficients, that is, low speed flight, and too little effective dihedral at the lower-than-design lift coefficients, that is, high speed flight. In other words, wing sweep contributes to the total aircraft effective or aerodynamic dihedral, and consequently the roll stability coefficient, and such effective dihedral changes as the lift coefficient of the wing is changed. This is not true of aircraft equipped with straight or unswept wings since the effective dihedral of such wing designs does not change as the lift coefficient changes. Since roll and yaw stability are related to one another, their coefficients must remain proportionate in order for the aircraft to remain roll-yaw stable. Sweep of the wing varies the roll coefficient, but does not significantly effect the yaw coefficient. Therefore, as the lift coefficient of a swept wing changes from its on-design value, the aircraft's roll-yaw stability degrades. As a result, swept-wing aircraft are roll-yaw stable only at the on-design criteria or selected lift coefficient and other means are utilized to provide stability throughout the remainder of the design envelope.
The present invention ties dihedral to the lift coefficient of a swept wing and varies the geometrical dihedral of such wing in relationship to the change in lift coefficient so as to obtain the desired roll-yaw stability throughout the entire flight envelope. While it is known that variable dihedral wings are disclosed in the prior art, for example, see U.S. Pat. Nos. 2,721,046 and 2,915,261, none of the known prior art designs tie the change in dihedral angle to the change in the lift coefficient of the airfoil, and none disclose means responsive to such changes in the airfoil lift coefficient for effecting a change in the geometric dihedral of the swept-wing aircraft so as to maintain a desired roll-yaw stability relationship as will be hereinafter explained.